My ABS light would come on when the car started to move after a startup.
ABS would not work
(1) The wheel speed sensors had not been cleaned in years so that was my first check. Removed and cleaned all four of them, and they were very dirty. Problem remained.
(2) Pulled and checked the ABS motor and valve relays, and diode. All were good.
(3) Disconnected the two ABS hydraulic unit connectors. The main control one had a little dry corrosion, cleaned it.
(4) Check voltages at hydraulic unit. They were good.
Reconnected everything and the problem went away and the brakes worked fine for two weeks. Then.

ABS light remain on after startup and before moving.
ABS would not work.
(1) Swapped ABS control units located in the left rear of the hatch area.
Problem remained.
(2) Check all ABS wiring from the rear control unit to the front hydraulic unit, and the voltages from the battery at the rear. All were good.
(3) Check out each sensor at the control unit, static and dynamic tests were done. All were good. Problem remained.
(4) Used a Mazda ABS checker. Ran the test three times and it would give different multiple problems every time but always said the LF solenoid was stuck open. But it never completed the complete test criteria as listed in the manual. Something is fishy! This did not make sense to me because neither the motor or solenoids were making any noise. Maybe the test unit had "SECRET and HIDDEN" analysis features not show in the schematics.
(5) Manually cycled the ABS motor and the three solenoids while the brake pedal was floored. All 4 functioned. Now I am getting pissed off! ABS still does not work.
(6) Removed the diode and replaced with a test diode. The problem remained so I reinstalled the stock diode.
(6) Checked the hydraulic unit voltages again at the ABS hydraulic unit. Now the 12 volts coming through the 15 amp ABS fuse was low, but it was fine before.
(7) Started testing the wires from the fuse to the hydraulic unit. Found that if I wiggled the 12v wire between the connector and the unit, the voltage would fluctuate.
(8) Pulled that pin out of the connector. It is a square box female design and the spring side was totally missing. One edge of the male pin was very slightly burned.
(9) Pulled the same type of female pin out of a new unused connector in my parts bin and repaired the connector. Evidently that one pin was not real tight and over the years the extra resistance slowly burned it up until it failed.
PROBLEM FOUND AND FIXED, ABS FUNCTIONS AGAIN.